Find the angle of inclination of the tangent to the graph of the function f (x) = 1+ sin x, drawn at the point M (n; 1)

We have a function:

y = 1 + sin x.

Let us find the angle of inclination of the tangent to the graph of the function with the abscissa at the point x0 = A.

The angle of inclination of the tangent to the graph of the function is found from its equation. Let’s write it down:

y = y ‘(x0) * (x – x0) + y (x0).

The angle of inclination is found as follows – its tangent is equal to the slope of a straight line, and in turn, the slope of a straight line is a factor in the variable, that is, y ‘(x0). Let’s find him.

y ‘(x) = cos x;

y ‘(x0) = cos П = -1.

A = arctan (-1) = 135 °.

The angle of inclination of the tangent is 135 °.